Time-Leveled Hypersoft Matrix, Level Cuts, Operators, and COVID-19 Collective Patient Health State Ranking Model

ABSTRACT

This article is the first step to formulate such higher dimensional mathematical structures in the extended fuzzy set theory that includes time as a fundamental source of variation. To deal with such higher dimensional information, some modern data processing structures had to be built. Classical matrices (connecting equations and variables through rows and columns) are a limited approach to organizing higher dimensional data, composed of scattered information in numerous forms and vague appearances that differ on time levels. To extend the approach of organizing and classifying the higher dimensional information in terms of specific time levels, this unique plithogenic crisp time-leveled hypersoft-matrix (PCTLHS matrix) model is introduced. This hypersoft matrix has multiple parallel layers that describe parallel universes/realities/information on some specific time levels as a combined view of events. Furthermore, a specific kind of view of the matrix is described as a top view. According to this view, i-level cuts, sublevel cuts, and sub-sublevel cuts are introduced. These level cuts sort the clusters of information initially, subject-wise then attribute-wise, and finally time-wise. These level cuts are such matrix layers that focus on one required piece of information while allowing the variation of others, which is like viewing higher dimensional images in lower dimensions as a single layer of the PCTLHS matrix. In addition, some local aggregation operators are designed to unify i-level cuts. These local operators serve the purpose of unifying the material bodies of the universe. This means that all elements of the universe are fused and represented as a single body of matter, reflecting multiple attributes on different time planes. This is how the concept of a unified global matter (something like dark matter) is visualized. Finally, to describe the model in detail, a numerical example is constructed to organize and classify the states of patients with COVID-19.